Why? How do you define interesting research directions? That used to be defined by testing the limits of human understanding i.e. some people can't figure something out. AI might have very different ideas about what is interesting and I am not sure what humans would get out of putting years into understanding AI proofs for what? What are we doing at that point? Like if you spend years understanding some AI proof of theorem 123456, why is that meaningful? I am actually asking why you think defining interesting research directions will stay relevant. In my opinion, people spend years acquiring knowledge so they can work on problems which is separate.
There's two points about this I am assuming 1) Mathematics actually has a significant subjectivity to it and is community oriented and not just climbing a never ending list of theorems that exists in the universe 2) A lot of mathematical research work is inside of a subfield and isn't directly motivated by applications. Sometimes it is but e.g. people don't work on obscure theorems about elliptic curves because of a dire need for that but more because the community found it interesting.
But the work the Mochizuki case generated can also be done by AI. AI could generate a landmark proof and then people could use it to solve or simplify intermediate problems and you could use a different AI prompt to try to disprove it if you were really skeptical. From my memory I think they said it took 88 hours to solve a Millenium Problem versus the decades of time humans have put into it.
I don't like nuance here. I think progress is really measured by what humans are able to do and understand, not machines. It is significant if we find problems we struggle to solve. That tells us something. What does it take for humans to solve these problems is related.
The best analogy I can give is if you wanted to climb Mt. Everest you might ask someone for guidance. Would it be better to ask someone who has climbed Mt. Everest or someone who took a helicopter ride up near the top and then went to the peak? This is like the AI versus human gap to me. The helicopter is like using AI to generate a proof. The person who actually climbed Mt. Everest has firsthand knowledge of the experience. Same thing for a difficult proof. The struggle people have is actually valuable here. Likewise, we know people are actually capable of climbing Mt. Everest but if they had only ever rode a helicopter to the top, the knowledge of climbing it would not exist, and surely that is meaningful knowledge given the risks.
So if we rely on AI for proofs I think we lose a sense of what is difficult and why. We lose a sense of what human achievement is. Surely climbing Mt. Everest means more than taking a helicopter up? For students, why bother grinding through all the material of climbing Mt. Everest and then attempting it if the helicopter ride is how things are done now? This would have the affect of destroying knowledge.
(please do not nitpick the analogy because it's the best but perhaps a clumsy way to describe my thoughts)
> From my memory I think they said it took 88 hours to solve a Millenium Problem versus the decades of time humans have put into it.
Keep in mind those ~88 hours were spread across ~10,000 simultaneous agent instances.
So, roughly 880,000 hours of compute.
Assuming a fifty-year career, and forty-hour workweeks, a human mathematician's career is about 100,000 hours of "compute".
I suspect that with six good mathematicians spending their whole careers primarily focused on it, and working together closely, Navier-Stokes might well have fallen already.
The perverse incentives of academia mean this has never occurred.
The perverse incentives of industry mean OpenAI intentionally scooped researchers who were getting close (granted, with AI help).
I'm not trying to dismiss the achievement - if the proof turns out to be solid, it's quite impressive (though much less so if the training data included the recent human breakthrough, which seems pretty plausible).
I'm just pointing out that "88 hours" is a very misleading way of framing this.
> I suspect that with six good mathematicians spending their whole careers primarily focused on it, and working together closely, Navier-Stokes might well have fallen already.
> The perverse incentives of academia mean this has never occurred.
This. Mathematicians in their most energetic years are trying to get tenure or land a tenure-track job. They are disincentivized to go all-in on ultra high risk, high-reward problems. The potential downside is just too forbidding. It's much safer to develop a research program in a mainstream field that affords many opportunities for partial progress that can translate to a robust publication record.
"I suspect that with six good mathematicians spending their whole careers primarily focused on it, and working together closely, Navier-Stokes might well have fallen already"
There were more than six doing that and it's essentially why it was ripe for AI to finish it off. But the finishing off was quicker than anyone expected
I'm not a mathematician, nor do I know almost anything about the discipline, but it sounds like maybe you do.
What teams of people spent an entire career working together, focused entirely on Navier-Stokes or problems they suspected were related, without any "publish or perish" concerns?
I realize tenure is a thing, but my limited understanding is that a significant amount of time is spent earning it, once you account for Ph.D. program and the years of needed to be granted it.
ok I realize this is a tangent but you're saying my post is very misleading and then also saying that a human mathematician's career is about 100,000 hours of compute and that Navier-Stokes could've had a solution by now if not for perverse incentives. You may be right but I don't think this is a great argument because in a year I would bet that those numbers change since computing power tends to increase or get cheaper over time. So I am taking the stance AI can outdo people if not now, perhaps soon.
I wasn't trying to say that genAI won't beat humans. It arguably already has, much as that may fill me with horror and revulsion.
I'm just trying to point out that economically, we have not yet reached the point where AI mathematics research is a no-brainer hands-down win, no consideration required.
It might already be a win, and certainly the ability to compress those 900,000 hours of effort into an actual week of linear time is mind-boggling and potentially a huge game-changer for all kinds of open research questions.
It's not obvious that human math research is dead yet.
I agree entirely with what you're saying, right up until your final question:
> why bother grinding through all the material of climbing Mt. Everest and then attempting it if the helicopter ride is how things are done now?
I think you answered this yourself earlier:
> I think progress is really measured by what humans are able to do and understand
People want to make this progress. Therefore people will "grind Everest" as a mathematical community, and that is maybe not so hugely different from a lot of previous mathematical work.
There's still ample room for creativity: simplifying, generalizing, asking new questions humans are interested in, ...
> Does this mean that we wouldn't have mathematicians or physicists or computer scientists or biologists anymore?
In the case of mathematicians, I think not as researchers. What would a research mathematician do? I don't think there would be any reason to try to gain insight from proofs that AI made for the sake of understanding. I don't see what that would achieve besides just retaining extremely niche knowledge (which AI or the oracle already does). The whole point of having that knowledge was to build toward novel work which the AI/oracle does. Also, the time spent and difficulty understanding them could be very high but with no payoff besides just understanding them because the AI/oracle would be used to solve all the problems anyway.
I don't get this argument. We skip over fixing the birthrate and instead rely on immigration. There's a whole bunch of reasons people give for why we can't fix it like costs, jobs, housing, etc. Ok, so then first wouldn't immigrants also have the same problem once they get here or do they have a way of bypassing our low birthrate somehow but then we were told we can't bypass it, it exists because of the costs, jobs. etc.
So the immigrants end up with the same birth rate and then we have to bring in more immigrants. So there would have to be a constant source of excess people somewhere else for this to be sustainable. So it gets to a point where I wonder if this is really the plan.
You're assuming the birthrate can be "fixed". Japan has an even worse demographic problem. They've tried "fixing" it and nothing much works. Similar for South Korea. Japan would certainly benefit from opening up to more immigration. Countries that can attract more immigration are going to benefit economically as the birthrates continue to decline globally. Why not be attractive to immigrants instead of wanting to repel them?
Make abortion and contraception illegal, and strongly enforce those laws.
It worked with Romania in the 1960s and 1970s. Mind you, it caused a bunch of other problems to crop up, but Romania did solve their low birth rate problem.
It worked: The birth rate exceeded the rate of deaths until Nicolae Ceausescu was overthrown in 1989. There was some level of circumvention in the 1970s and 1980s, but birth rates continued to outpace death rates up until the day Ceausescu was overthrown and Decree 770 was made null and void. (If you have a different definition of “work” than “it increased fertility”, please let me know what that definition is)
Mind you, as I said before, there were a lot of undesirable, shall we say, side effects because of this decree, but it did solve the fertility problem.
{Snark tag: Obviously, I do not endorse doing something as Orwellian as having a government like the Romania of the 1960s and 1970s, and the unwanted kids caused a huge amount of intergenerational trauma. To get back to the issue of fertility collapse, fertility collapse is an issue which will last only one generation: The people who have kids will have worldviews which encourage having more children}
No, very clearly in the graph in that link it only bumped the rate of births for about 3 years before it very clearly returned to it's previous trajectory.
It did not change the overall trend because radical anti-abortion measures like that do not change people's desire to have kids.
As one can see, births were at or above pre-decree levels after Decree 770 was passed, and only went below pre-decree levels when the decree was dismantled in 1989. The 1970s downward slope is much less steep than the 1960s pre-decree downward slope. In the 1980s, there was no downward slope whatsoever. Fertility stayed at roughly pre-decree levels before plummeting once the decree was ended. At no point while Decree 770 was in effect did we have a birthrate that “very clearly returned to it's [sic] previous trajectory”.
Now, let’s go back to what I was replying to when I brought up Decree 770. “Our birthrate has been below replacement” said one poster, and in a reply “You're assuming the birthrate can be "fixed"”. Decree 770 fixed the issue I was replying to: Birthrate being below replacement. Pre-decree, Romania’s birthrate was on a downward path, and would had been below death rates by the early 1970s. Because of the decree, the birth rate stayed above replacement rates until it was repealed in 1989.
Decree 770 increased fertility. It kept fertility above death rates. I have already posted elsewhere why Decree 770 was a very bad idea.
This will be my final reply to @mrguyorama. They do not come off as someone willing to admit when they are wrong about something.
I mention fertility rates remained constant in the 1980s. Now I know why fertility rates didn’t go down back in that era.
In the year 1984, Romania took a page from Orwell’s 1984: All medical units were put under surveillance to minimize the number of illegal abortions. There was now a secret “Thought Police” in 1984 monitoring all doctors and nurses to make sure no abortions slipped through the cracks. The number of abortion related convictions in 1986 doubled compared to 1985. Just like 1984, not only did a hidden thought police find these people doing illegal abortions, but people would report on their neighbors.
Romania was able to stop the 1970s fertility decline (which, again, was a good deal less steep than the fertility decline when abortions were legal) in the 1980s by going full Orwell and clamping down the screws.
It’s probably a bad prediction of the future, but having an exaggerated dystopian view of the future is a classic trick used in golden age science fiction (e.g. Decision at Doona from 1969 had a grossly overpopulated Earth) so one I was able to accept while reading the story.
It definitely has a bias; it doesn’t mention the stories of women regretting abortions at all, except (minor spoiler) mentioning that Asenath Smith didn’t want an abortion. As someone who has had multiple women confide their abortion stories to me, it’s quite common for women to deeply regret having them. I understand why a story as political as this one doesn’t want to get in to the nuance of the trauma abortion can cause, because it’s written in the same year Roe vs. Wade was overturn, so it’s a story of how much women need access to pregnancy tests and to abortion. [1]
[1] I personally believe in the right to an abortion, for the simple reason that, when a woman has a miscarriage or a baby which just isn’t viable, the medical treatment she gets should be a decision doctors make, not a decision people with guns and cages make.
The “proposed solutions” are very misogynistic. They include repealing the 19th amendment (not letting women vote), repealing sex discrimination laws, and enforcing “patriarchy”. See, for example https://archive.ph/20260624060135/https://nitter.net/Schtal2... for the kind of nonsense these kinds of people are proposing, based on lies and fabrications.
I know what some X users say about that, and I know that some people here have these same ideas. I was just wondering if that is the supposed solution that the person suggested
You’ll have to ask @account42, but I will bet you it’s the same answer I came up with: Take away people’s freedoms and have a hard, strongly enforced (i.e. Orwellian levels of enforcement) ban on contraception and abortions.
Both @account42 and myself agree this isn’t a particularly good solution, and I’m not worried about the fertility collapse myself: It is an issue which will last for only one generation.
I'm not sure if they agree with you that is not a good solution, though. I don't even consider it a solution the same way that I don't consider slavery a solution for lack of workers.
Here is what they said: “You can definitely fix it. You might not like what it takes but others don't like their culture being replaced either.”
I think he’s implying he has some pretty, shall we say, interesting views on the matter. As someone who has been in an interracial marriage and multiple interracial relationships, I probably don’t agree with those particular views.
It would be nice to know what he’s advocating for, but he’s gotten pretty mum after I pointed out it could be done, but only with Orwellian levels of suppression.
Teenage pregnancy, limited rights for unmarried women, heavily surveilled birth-control usage, all that good stuff. So long as the culture is preserved! There are 14 words that basically sum it all up
Yes, the only way to preserve USAs culture of freedom of the individual is to dissuade/force women from making choices that dont benefit the group. Else we will fall to communism!!
It is very much possible to use government force to solve the birthrate problem. Romania did it in the 1960s. Mind you, this would cause a lot of misery and suffering but it has been done.
Well arguably H-1B is being abused specifically to lower wages. I think we're aware especially given the contrived ways of circumventing how H-1B is supposed to be used like deliberately advertising jobs in an obscure print newspaper that doesn't even get circulated or modifying the job description to suit an international candidate alone.
This is one of the problems with this issue. People talking about it are pretty clueless and have no idea what they're talking about. They get whipped up into an ignorant frenzy about something they don't understand. H-1B has no requirement for advertising in newspapers.
>But for me, a larger concern is elite overproduction.
Props for finding incredibly niche and out-there theories to support your worldview. This is kind of nice about HN. Normally, people would just cite the great replacement theory or other leftist slop to support protectionism, but you found something even more bizarre. It reminds me of how Vance talks. He'll bring up latin incantations like ordo amoris to justify otherwise mundane cruelties.
> They get whipped up into an ignorant frenzy they don't understand. H-1B has no requirement for advertising in newspapers.
Oh yes, yeesh, my bad, this is for green cards only, there's some hilariously low bar for H-1B yet it still exists. But let's just go back to my point that H-1B is used to lower wages. You can just search for it unless you think it's a conspiracy theory. For all your frothing hostility, I noticed you didn't try to defend lowered wages. What are you defending here? Corporate profits? Some kind of moral issue? Do you have evidence H-1B was vitally necessary?
> incredibly niche and out-there theories
It's a scientific theory.
> support protectionism
I think that misses the point if you mean trade protectionism. I am saying H-1B (also EB-2 and other degree to green card pipelines) presents a danger of destabilizing society. I already think that's obviously the case.
Everything is used to lower wages. Uber, waymo, doordash, LLMs, etc. all reduce wages. There is no requirement in the statute that it should not lower wages. Congress considered the tradeoff and decided that it was worth having the program. It is a minuscule number, btw. 85k per year, which given the size of the US economy should not even register anywhere in any discussions. In any case, these econ 101 discussions are beyond the scope here.
Congress did that for when skilled jobs couldn't be filled. It wasn't primarily meant to just onboard people and fill jobs. I don't think ~85k per year is minuscule. I think that is substantial and the cap has regularly been exceeded and this is annually for decades.
That brings us to
Americans are too dumb to get these jobs so we still need it:
If that's true, which I doubt, I am not sure why this isn't a higher priority problem of ours to solve.
Americans are not too dumb but we need H-1B anyway for reasons:
>the cap has regularly been exceeded and this is annually for decades.
The cap is 85k, which is never exceeded, as that is a statutory limit. There are other cap exempt categories for non-profits and universities.
>That brings us to
It doesn't bring us to any of these conclusions. The vehicle for the change you seek is the legislature. Lobby Congress to change the law. You have a house rep and 2 state senators. Talk to them about your concerns.
Those are exactly the two conclusions it brings us to. If a skilled job can't be filled the question becomes why the skill gap exists or if it even exists at all and I have never seen someone suggest every single job given to a H-1B holder provably could not be filled by a citizen. There's almost no bar at all besides putting a notice in the lunch room or something equally frivolous. The LCA is easily gamed.
>the vehicle for change you seek is the legislature
I never argued the fee was legal for reference. And oop must've forgotten that Congress cared about my concerns, thanks for the tip!
You are building up hypotheses and theories in your head that have no basis in reality. There is no requirement that a job is opened up to H-1B if a citizen cannot do it. That does not exist. You are starting with this flawed assumption and then reaching some absurd conclusions. H-1B exists because it is nice to have and provides positive value. The fact that it may displace other citizens' jobs is fine too and permitted by the statute. Uber doesn't exist because no capable taxi drivers could ride a cab. Your grievance stems from a flawed premise. You wish there were protectionism, but there is no protectionism in the law. So again, talk to Congress. And Congress knows very well how to do protectionism. See Jones Act.
You know what? You might be right. The wording doesn't seem to specifically state anything about reasons indeed implying that "H-1B exists because it is nice to have and provides positive value". The lore about requirements doesn't appear. This means the law was never intended to fill shortages and the law isn't really being gamed because there's nothing dishonest about the intentions. This saddens me greatly. Truly the only fix is through Congress.
I think people misunderstand what democracy is. To many people they think democracy is a resistance against, ultimately, the Nazis again. The West is structured this way. Post WWII we had a quiet revolution around this. It seems so ingrained people don't even think about it.
To many people, they believe there is a constant and persistent threat of Nazis and that it is the duty of enlightened government officials to continuously stage interventions to stop them. They think people are the problem so it is good to be totalitarian. It is kind of a type of paranoia it's just widely accepted as fact and it's a part of Western institutional ethos.
Some state-resistant technology (idk if this term is in general use) like Signal planned for a lot of contingencies that could happen caused by governments. Tor is kind of like that too. So I have more optimism for building tech that is state-resistant than I do for any kind of constitution, or movement, or law. That's not to say give up but I think it's hard to argue against a state.
> Anyone who brings up kids is trying to manipulate you into giving up your freedom
These are NGOs not parents. And "child safety" is often a euphemism. The point is it's hard to argue against child safety. For example, if opaque NGOs demand deanonymization to stop CSAM, I am assuming most people would not want to seem like they are in favor of CSAM. So you need an organized effort to argue in favor of privacy and even then anyone who does it can easily be smeared as a CSAM user. So child safety can backdoor something else.
There's two points about this I am assuming 1) Mathematics actually has a significant subjectivity to it and is community oriented and not just climbing a never ending list of theorems that exists in the universe 2) A lot of mathematical research work is inside of a subfield and isn't directly motivated by applications. Sometimes it is but e.g. people don't work on obscure theorems about elliptic curves because of a dire need for that but more because the community found it interesting.
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